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Based on a system of $J$ number of unstable non-BPS D0-branes of
type IIB theory in the light-cone gauge and on the plane-wave
background, we construct a 1-parameter family of 0+1-dimensional
$U(J)$ gauge theories in the form of supersymmetric matrix quantum
mechanics. This configuration suffers from tachyonic instability
which dynamically stabilizes through the process of open string
tachyon condensation. At the true extrema of the effective potential
and by taking kinematical low energy limit to decouple the heavy
modes, it leads to a Matrix theory which we propose to be the
discrete light-cone quantization (DLCQ) of type IIB string theory in
the sector with $J$ units of light-cone momentum on the AdS (and/or
plane-wave) background. At the minima, where the tachyon has been
condensed, non-BPS D0-branes have been blown up to configurations of
fuzzy 3-spheres which go over to BPS spherical D3-brane giant
gravitons in the string theory (continuum) limit
$J\rightarrow\infty$.
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